Computer aided geometric design is the design and representation of curves, surfaces, and volumes in an interactive computer graphics environment. This project focuses on design and will include work in two areas: (1) geometry processing and (2) nonuniform rational B-splines (NURBS). Geometry processing is the calculation of geometric properties of curves and surfaces. NURBS are becoming a de facto industry standard for geometry representation because both polynomials and conics can be represented exactly. Both areas are of prime importance in many fields such as computer aided design/computer aided manufacturing. Both areas also have considerable theoretical interest as well. Research subtopics under these two principal headings include the following: (1) surface/surface intersection, offset surfaces, surface triangulations and (2) curve and surface fairing, automatic weight generation for NURBS, and the investigation of stabiblity issues associated with rational shape representations.
